SOLDOTNA, Alaska—Since joining the Alaskan oil rush in the early 1980s, Richard Repper has jumped from project to project in the state, with no job more than a three-hour flight from this town about 70 miles south of Anchorage.

But last fall, he began working in North Dakota, more than 2,000 miles away. A construction manager for an oil-field-services company, the 60-year-old Mr. Repper is finding more opportunity in the Bakken Shale...